Gauge Theory · April 2026
The Standard Model Has One Address
The Standard Model gauge numbers 4, 3, 8 are derived from the character table of the binary icosahedral group 2I. Three-phase cascade. 60 fermion modes equal 60 boson modes exactly. The SM lives at one address in the representation theory of 2I.
Key Results
The gauge numbers are not chosen — they are read off
The binary icosahedral group 2I has a unique character table with 9 irreducible representations. The SM gauge structure follows from reading the table: ρ₂ = quark, ρ₃ = lepton, ρ₄ = colour (3), ρ₇ = γ W⁺ W⁻ Z (4 EW bosons), ρ₄ ⊗ ρ₄ = 1 + 3 + 5 → 8 gluons. The three-phase condition 1 + ω + ω² = 0 enforces confinement.
1
ρ₂ = quark (dim 2), ρ₃ = lepton (dim 3), ρ₄ = colour (dim 4 → 3 colours after projection). All from 2I character table.
2
ρ₇ (dim 4) = γ, W⁺, W⁻, Z — the four electroweak bosons. Not fitted: the dimension of ρ₇ is the number of EW bosons.
3
ρ₄ ⊗ ρ₄ = ρ₁ + ρ₃ + ρ₅ = 1 + 3 + 5 → adjoint of SU(3) has dimension 8. Eight gluons from one tensor product.
4
60 fermion modes (ρ₂ ⊗ ρ₃ contributions) = 60 boson modes exactly. Fermion-boson balance is a theorem of 2I, not supersymmetry.
Kill Conditions
K1: A fourth colour confirmed at LHC → ρ₄ assignment fails
K2: A fifth EW boson discovered → ρ₇ dim-4 assignment fails
K3: Fermion-boson count found unequal in SM → 60/60 balance fails